/// <summary>
/// Creates a matrix for rotating points around the Y-axis.
/// </summary>
/// <param name="radians">The amount, in radians, by which to rotate around the Y-axis.</param>
/// <returns>The rotation matrix.</returns>
public static FixMatrix4x4 RotateY(Fix64 radians)
{
FixMatrix4x4 result;
Fix64 c = FixMath.Cos(radians);
Fix64 s = FixMath.Sin(radians);
// [ c 0 -s 0 ]
// [ 0 1 0 0 ]
// [ s 0 c 0 ]
// [ 0 0 0 1 ]
result.M11 = c;
result.M12 = Fix64.Zero;
result.M13 = -s;
result.M14 = Fix64.Zero;
result.M21 = Fix64.Zero;
result.M22 = Fix64.One;
result.M23 = Fix64.Zero;
result.M24 = Fix64.Zero;
result.M31 = s;
result.M32 = Fix64.Zero;
result.M33 = c;
result.M34 = Fix64.Zero;
result.M41 = Fix64.Zero;
result.M42 = Fix64.Zero;
result.M43 = Fix64.Zero;
result.M44 = Fix64.One;
return(result);
}
/// <summary>
/// Creates a matrix for rotating points around the Y-axis, from a center point.
/// </summary>
/// <param name="radians">The amount, in radians, by which to rotate around the Y-axis.</param>
/// <param name="centerPoint">The center point.</param>
/// <returns>The rotation matrix.</returns>
public static FixMatrix4x4 RotateY(Fix64 radians, FixVector3 centerPoint)
{
FixMatrix4x4 result;
Fix64 c = FixMath.Cos(radians);
Fix64 s = FixMath.Sin(radians);
Fix64 x = centerPoint.x * (Fix64.One - c) - centerPoint.z * s;
Fix64 z = centerPoint.x * (Fix64.One - c) + centerPoint.x * s;
// [ c 0 -s 0 ]
// [ 0 1 0 0 ]
// [ s 0 c 0 ]
// [ x 0 z 1 ]
result.M11 = c;
result.M12 = Fix64.Zero;
result.M13 = -s;
result.M14 = Fix64.Zero;
result.M21 = Fix64.Zero;
result.M22 = Fix64.One;
result.M23 = Fix64.Zero;
result.M24 = Fix64.Zero;
result.M31 = s;
result.M32 = Fix64.Zero;
result.M33 = c;
result.M34 = Fix64.Zero;
result.M41 = x;
result.M42 = Fix64.Zero;
result.M43 = z;
result.M44 = Fix64.One;
return(result);
}
public FixVec2 Rotate(Fix degree)
{
var cos = FixMath.Cos(degree);
var sin = FixMath.Sin(degree);
return(new FixVec2(X * cos - Y * sin, X * sin + Y * cos));
}
/// <summary>
/// Creates a matrix for rotating points around the X-axis, from a center point.
/// </summary>
/// <param name="radians">The amount, in radians, by which to rotate around the X-axis.</param>
/// <param name="centerPoint">The center point.</param>
/// <returns>The rotation matrix.</returns>
public static FixMatrix4x4 RotateX(Fix64 radians, FixVector3 centerPoint)
{
FixMatrix4x4 result;
Fix64 c = FixMath.Cos(radians);
Fix64 s = FixMath.Sin(radians);
Fix64 y = centerPoint.y * (Fix64.One - c) + centerPoint.z * s;
Fix64 z = centerPoint.z * (Fix64.One - c) - centerPoint.y * s;
// [ 1 0 0 0 ]
// [ 0 c s 0 ]
// [ 0 -s c 0 ]
// [ 0 y z 1 ]
result.M11 = Fix64.One;
result.M12 = Fix64.Zero;
result.M13 = Fix64.Zero;
result.M14 = Fix64.Zero;
result.M21 = Fix64.Zero;
result.M22 = c;
result.M23 = s;
result.M24 = Fix64.Zero;
result.M31 = Fix64.Zero;
result.M32 = -s;
result.M33 = c;
result.M34 = Fix64.Zero;
result.M41 = Fix64.Zero;
result.M42 = y;
result.M43 = z;
result.M44 = Fix64.One;
return(result);
}
/// <summary>
/// Creates a matrix for rotating points around the Z-axis, from a center point.
/// </summary>
/// <param name="radians">The amount, in radians, by which to rotate around the Z-axis.</param>
/// <param name="centerPoint">The center point.</param>
/// <returns>The rotation matrix.</returns>
public static FixMatrix4x4 RotateZ(Fix64 radians, FixVector3 centerPoint)
{
FixMatrix4x4 result;
Fix64 c = FixMath.Cos(radians);
Fix64 s = FixMath.Sin(radians);
Fix64 x = centerPoint.x * (1 - c) + centerPoint.y * s;
Fix64 y = centerPoint.y * (1 - c) - centerPoint.x * s;
// [ c s 0 0 ]
// [ -s c 0 0 ]
// [ 0 0 1 0 ]
// [ x y 0 1 ]
result.M11 = c;
result.M12 = s;
result.M13 = Fix64.Zero;
result.M14 = Fix64.Zero;
result.M21 = -s;
result.M22 = c;
result.M23 = Fix64.Zero;
result.M24 = Fix64.Zero;
result.M31 = Fix64.Zero;
result.M32 = Fix64.Zero;
result.M33 = Fix64.One;
result.M34 = Fix64.Zero;
result.M41 = Fix64.Zero;
result.M42 = Fix64.Zero;
result.M43 = Fix64.Zero;
result.M44 = Fix64.One;
return(result);
}
public void SinWorks(double value)
{
var expected = Math.Sin(value * Math.PI / 180.0);
var result = (double)FixMath.Sin((Fix)value);
Assert.AreEqual(expected, result, (double)Fix.Epsilon);
}
public static FixTrans2 MakeRotation(Fix radians)
{
var cos = FixMath.Cos(radians);
var sin = FixMath.Sin(radians);
return(new FixTrans2(
cos, -sin, 0,
sin, cos, 0
));
}
public void Set(Fix degrees)
{
Fix c = FixMath.Cos(degrees);
Fix s = FixMath.Sin(degrees);
m00 = c;
m01 = -s;
m10 = s;
m11 = c;
}
public static FixTrans3 MakeRotationX(Fix degrees)
{
var cos = FixMath.Cos(degrees);
var sin = FixMath.Sin(degrees);
return(new FixTrans3(
1, 0, 0, 0,
0, cos, -sin, 0,
0, sin, cos, 0
));
}
/// <summary>
/// Constructs a quaternion from a vector3.
/// https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
/// </summary>
/// <param name="vector">The vector3 being converted.</param>
public FixQuaternion(FixVec3 vector)
{
w = FixMath.Cos(vector.z / 2) * FixMath.Cos(vector.y / 2) * FixMath.Cos(vector.x / 2)
+ FixMath.Sin(vector.z / 2) * FixMath.Sin(vector.y / 2) * FixMath.Sin(vector.x / 2);
x = FixMath.Cos(vector.z / 2) * FixMath.Cos(vector.y / 2) * FixMath.Sin(vector.x / 2)
- FixMath.Sin(vector.z / 2) * FixMath.Sin(vector.y / 2) * FixMath.Cos(vector.x / 2);
y = FixMath.Sin(vector.z / 2) * FixMath.Cos(vector.y / 2) * FixMath.Sin(vector.x / 2)
+ FixMath.Cos(vector.z / 2) * FixMath.Sin(vector.y / 2) * FixMath.Cos(vector.x / 2);
z = FixMath.Sin(vector.z / 2) * FixMath.Cos(vector.y / 2) * FixMath.Cos(vector.x / 2)
- FixMath.Cos(vector.z / 2) * FixMath.Sin(vector.y / 2) * FixMath.Sin(vector.x / 2);
}
public FixTrans2(FixVec2 position, FixVec2 scale, Fix rotation)
{
var cos = FixMath.Cos(rotation);
var sin = FixMath.Sin(rotation);
_m11 = cos * scale.X;
_m12 = -sin * scale.X;
_m13 = position.X;
_m21 = sin * scale.Y;
_m22 = cos * scale.Y;
_m23 = position.Y;
}
/// <summary>
/// Creates a matrix which rotates around the given axis by the given angle.
/// </summary>
/// <param name="axis">The axis.</param>
/// <param name="angle">The angle.</param>
/// <param name="result">The resulting rotation matrix</param>
public static void AxisAngle(ref FixVector3 axis, Fix64 angle, out FixMatrix4x4 result)
{
// a: angle
// x, y, z: unit vector for axis.
//
// Rotation matrix M can compute by using below equation.
//
// T T
// M = uu + (cos a)( I-uu ) + (sin a)S
//
// Where:
//
// u = ( x, y, z )
//
// [ 0 -z y ]
// S = [ z 0 -x ]
// [ -y x 0 ]
//
// [ 1 0 0 ]
// I = [ 0 1 0 ]
// [ 0 0 1 ]
//
//
// [ xx+cosa*(1-xx) yx-cosa*yx-sina*z zx-cosa*xz+sina*y ]
// M = [ xy-cosa*yx+sina*z yy+cosa(1-yy) yz-cosa*yz-sina*x ]
// [ zx-cosa*zx-sina*y zy-cosa*zy+sina*x zz+cosa*(1-zz) ]
//
Fix64 x = axis.x, y = axis.y, z = axis.z;
Fix64 sa = FixMath.Sin(angle), ca = FixMath.Cos(angle);
Fix64 xx = x * x, yy = y * y, zz = z * z;
Fix64 xy = x * y, xz = x * z, yz = y * z;
result.M11 = xx + ca * (Fix64.One - xx);
result.M12 = xy - ca * xy + sa * z;
result.M13 = xz - ca * xz - sa * y;
result.M14 = Fix64.Zero;
result.M21 = xy - ca * xy - sa * z;
result.M22 = yy + ca * (Fix64.One - yy);
result.M23 = yz - ca * yz + sa * x;
result.M24 = Fix64.Zero;
result.M31 = xz - ca * xz + sa * y;
result.M32 = yz - ca * yz - sa * x;
result.M33 = zz + ca * (Fix64.One - zz);
result.M34 = Fix64.Zero;
result.M41 = Fix64.Zero;
result.M42 = Fix64.Zero;
result.M43 = Fix64.Zero;
result.M44 = Fix64.One;
}
public void SinAverageDeviationTest()
{
var totalDiff = 0.0;
var maxDiff = double.MinValue;
for (var i = 0; i < 3600; i++)
{
var fixAngle = FixMath.Pi * i / 1800;
var doubleAngle = Math.PI * i / 1800.0;
var diff = Math.Abs((double)FixMath.Sin(fixAngle) - Math.Sin(doubleAngle));
totalDiff += diff;
maxDiff = Math.Max(maxDiff, Math.Abs(diff));
}
// Max & Average deviation
FixAssert.AssertEquals(maxDiff, 0, 0.019f);
FixAssert.AssertEquals(totalDiff / 360, 0, 0.07f);
}
public static DynValue sin(ScriptExecutionContext executionContext, CallbackArguments args)
{
return(exec1(args, "sin", (x) => - FixMath.Sin(x * 360)));
}